French police search Vincennes forest on the outskirts of Paris after body parts were discovered. Photograph: Kenzo Tribouillard/AFP/Getty Images

When joggers stumbled over the footless and decomposing leg of a woman partially hidden by leaves and soil in a forest on the outskirts of Paris a fortnight ago French detectives were baffled.

Days later, when a guide dog uncovered the headless, limbless torso of a man at the foot of nearby trees, investigators knew they had entered what one officer described as "the realm of the sordid".

Knowing that without the missing heads, hands or feet, they would struggle to identify the cadavers, police searched the Vincennes forest for further remains.

Officers admitted they were "perplexed … and without even the beginning of a lead."

This week the mystery behind the macabre discoveries was apparently solved when a Chinese couple walked into a Paris police headquarters and reportedly confessed to a grim double murder, declaring themselves "overcome with remorse".

In a further twist the alleged killers told horrified detectives they had also disposed of the dead body of their victims' three-month-old baby in a rubbish bin near their Paris home.

The couple, named only as Lu, 30, and his wife Hui, 31, a student beautician, are due to appear before a judge on Tuesday to be formally put under investigation – the equivalent of being charged.

In an alleged confession said to have been detailed but confused, the pair told police a row had erupted after they agreed to look after the three-month-old baby of another Chinese couple overnight on 23 May. When the parents returned the next morning to collect their son, named Lucas, they were told he had died mysteriously in the night.

"Under questioning the woman explained that the child had been the victim of cot death," a police source told Le Parisien newspaper. "When the parents turned up there was a very heated discussion."

The newspaper said Hui told police that when she suggested paying the couple "damages" for the loss of their child, the mother tried to strangle her. During the row that followed the grieving father found a kitchen knife and stabbed Lu in the arm.

What ensued, according to police reports, is like a scene from the 1994 diabolic cult film Shallow Grave.

Le Parisien quoted an investigator as saying: "She [Hui] told us she had grabbed an axe before killing the baby's mother, then the father. She then cut up the bodies of the two victims in the bathroom before burying the remains with the help of her partner in the wood at Vincennes on the night of 24-25 May."

The alleged killers, who have a two-year-old son, cleaned their apartment so thoroughly that police, alerted by one of the victims' relatives, found no trace of blood. Then they fled to China. They returned to Paris 10 days later and sought advice from a lawyer who "strongly suggested" they go to police. On Saturday the pair turned up at 36 quai des Orfèves, the Paris equivalent of Scotland Yard, and turned themselves in.

Based on information the couple gave to the police, further body parts were found in the wood at the weekend. Detectives with dogs and diggers are still combing Vincennes for further evidence.

"The mystery of these human torsos could have gone on for a long time without these confessions," a source close to the inquiry told French journalists.

"It could have taken months, years even, to be solved. Now it is perhaps being resolved."

He added: "We're in the realm of the sordid."

The discovery of the decomposing leg in Vincennes on 8 June caused fear in France, coming shortly after the arrest of Luka Rocco Magnotta, the Canadian man suspected of dismembering a former lover in Montreal before fleeing to France and then Berlin.